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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 263, Pages 159–172
(Mi tm790)
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This article is cited in 1 scientific paper (total in 1 paper)
Toric Kempf–Ness Sets
T. E. Panovab a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
In the theory of algebraic group actions on affine varieties, the concept of a Kempf–Ness set is used to replace the categorical quotient by the quotient with respect to a maximal compact subgroup. Using recent achievements of “toric topology”, we show that an appropriate notion of a Kempf–Ness set exists for a class of algebraic torus actions on quasiaffine varieties (coordinate subspace arrangement complements) arising in the Batyrev–Cox “geometric invariant theory” approach to toric varieties. We proceed by studying the cohomology of these “toric” Kempf–Ness sets. In the case of projective nonsingular toric varieties the Kempf–Ness sets can be described as complete intersections of real quadrics in a complex space.
Received in March 2008
Citation:
T. E. Panov, “Toric Kempf–Ness Sets”, Geometry, topology, and mathematical physics. I, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 263, MAIK Nauka/Interperiodica, Moscow, 2008, 159–172; Proc. Steklov Inst. Math., 263 (2008), 150–162
Linking options:
https://www.mathnet.ru/eng/tm790 https://www.mathnet.ru/eng/tm/v263/p159
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Abstract page: | 300 | Full-text PDF : | 70 | References: | 49 | First page: | 8 |
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